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Supplementary Information
An actively ultrafast tunable giant slow-light
effect in ultra-thin nonlinear metasurfaces
Cuicui Lu,† Xiaoyong Hu,†,‡,* Kebin Shi,†,‡ Qin Hu,† Rui Zhu,†,‡ Hong Yang,† and Qihuang
Gong†,‡
†
State Key Laboratory for Mesoscopic Physics & Department of Physics, Peking University,
Beijing 100871, People’s Republic of China
‡
Collaborative Innovation Center of Quantum Matter, Beijing 100871, People’s Republic of
China
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The supplementary information includes:
I. Discussion of selecting structure parameters of the metasurface
II. Sample fabrication
III. Micro-spectroscopy measurement system
IV. Calculation methods for group index ng
V. Calculated linear transmission spectra of the metasurface with different structural parameters
VI. Optical interference experiment setup and measurement process
VII. Femtosecond pump-probe experiment setup and measurement process
VIII. Closed-aperture Z-scan measurements and discussion of nonlinearity
VIIII. AFM images for ZnO nanoparticles on ITO nanograin film and gold film
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I. Discussion of selecting structure parameters of the metasurface
1). The reason for selecting the equilateral triangle structure
The choice for the equilateral triangle structure comes from the following aspects. Firstly, we
want to achieve giant slow light effect. Gold rectangles have been investigated in many papers,
and the group index for gold rectangles is not large. While, few works of slow light effect on
triangle are found, and the curiosity on triangles encouraged us to investigate. Secondly, we want
to achieve large optical nonlinearity to reduce the pump power for ultrafast optical tunability.
Gold triangles have stronger surface plasmon polariton resonances according to our previous
work (see Cuicui Lu, et al. Plasmonics, 7, 159 (2011)). Thirdly, it is flexible to use triangle dimer
to achieve different slow light effect through changing the gap between the two triangles or the
structure parameters. Fourthly, other triangle shapes, such as right triangles, acute triangles or
obtuse triangles, also have some similar optical properties, however, all of these triangle shapes
include at least one sharp angle which is very difficult for nano-fabrications, so equilateral is a
trade-off choice.
2) The reason for selecting the gold nanoprism thickness of 40 nm
The choice of the effective thickness of 40 nm for gold nanoprisms is based on the following
considerations. Firstly, the penetration depth of gold in the near-infrared range has an order of 20
nm, the effective thickness should be larger than the penetration depth in order to obtain obvious
metamaterial induced transparency effect, and avoid the transmission of the probe light directly.
This results in a larger thickness for gold nanoprisms. Secondly, from the aspect of the practical
nano-fabrication, it is very difficult to maintain the perfect structure parameters of gold
nanoprisms for a large gold thickness. The larger of the gold thickness, the more obtuse of the
corners will be. Then, the triangles will be deformed seriously. This requires that the gold
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thickness should be as thin as possible. Considering the above factors, we have to select 40 nm as
the gold thickness.
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II. Sample fabrication
High-conductivity ITO layer was deposited on SiO2 substrate by using radio frequency sputtering
in an oxygen/argon plasma with a mixing ratio of 1:140 at a temperature of 500 °C. The
resistance was about 8 Ω/square for the high-conductivity ITO layer. The single layer graphene
was fabricated using the chemical vapor deposition (CVD) method.S1 An electron-beam
lithography system (Model Raith E-line, Raith Company, Germany) was used to prepare the
periodic patterns of the metasurface. The gold film was fabricated by using a laser molecular
beam epitaxy (LMBE) growth system (Model LMBE 450, SKY Company, China). The beam
(with a wavelength of 248 nm and a pulse repetition rate of 5 Hz) output from an excimer laser
system (Model COMPexPro 205, Coherent Company, USA) was used as the excitation light
source. The beam was focused onto a gold target mounted on a rotating holder, 15-mm away
from the substrate. The typical energy density of the excitation laser was about 500 mJ/cm2. The
growth rate measured by a film thickness/rate monitor was about 0.01 nm/pulse. The growth
process was conducted under a pressure of 6.5×10-4 Pa for gold films. The ZnO nanoparticles
were synthesized by zinc acetate dihydrate and potassium hydroxide in methanol according to the
literature procedures.S2,S3 The resulting ZnO nanoparticles were washed twice with methanol.
Finally, chloroform, ethylalcohol and 2-ethoxyethanol were added to disperse the ZnO
nanoparticles and reach a concentration of 0.7 mg/ml. The ZnO nanoparticles were prepared by
spin coating the ZnO dispersion solution onto the ITO substrate at 3,000 r/min for 20 s. The spincoating method was adopted for the fabrication of the multilayer sheets of graphene by using the
graphene dispersion solution in ethanol with a concentration of 0.2 mg/ml. The spin-coating
speed and the time were 1500 r/min and 30 s.
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III. Micro-spectroscopy measurement system
Micro-spectroscopy measurement experimental setup is shown in Fig. S1. A wideband white
light source ranging from 880 nm to 1760 nm (Model HL-2000, Ocean Optics) was normally
incident on the sample with a Y-polarized direction, i.e. the electric field is parallel to the ydirection of the structure in Figure.1c. The beam radius was focused to 100 μm. The transmission
light was collected by a long working distance objective (Mitutoyo 20, NA = 0.58) and then
detected using a fiber monochromator (Model NIR-512, Ocean Optics, USA) with a resolution of
0.74 nm, the output signal of which was collected and analyzed by a computer. The final obtained
tranmission spectrum was normalized with respect to a 40-nm-thick gold film coated on a 180nm-thick ITO film on SiO2 substrate, which is the standard method to study the transmission
properties of photonic metamaterials.
Beam
Splitter
Figure S1. Micro-spectroscopy measurement experimental setup.
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IV. Calculation methods for group index ng
Numerical simulations were performed by using the commercial finite element method
(FEM) solver of COMSOL Multiphysics. The permittivity of the gold was calculated as a
function of the wavelength using interpolation fitting and was taken from Ref. S4. Here, the
three-dimensional frequency domain module was used. The calculation of group refractive
index is based on the formula (1) and (2).
n

c
x  t
(1)
dn
d
(2)
ng  n  
where φ is the phase of the electric field, n is the phase refractive index. The phase change
can be extracted through COMSOL software, and then the group refractive index ng can be
calculated through formulae (1) and (2). From formula (1), for the output and input planes,
we can obtain
  n

c
x
(3)
so we obtain
n 
c

x
(4)
where Δx is the thickness of the metasurface, Δφ is the phase change,  is incident light
frequency, c is the light velocity in the vacuum.
From foumula (2), we can obtain
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ng 
d (n )
d
(5)
Substituting fomula (4) into fomula (5), we obtain
ng 
c d ( )
x d 
(6)
Δφ can be given by the numerical calculation result using the software of COMSOL Multiphysics.
In the COMSOL software, we wrote the expression “arg(emw.Ey)” to calculate the phase for
each plane under Y-polarized incident light.
According to the above calculations, we obtain the numeical simulation result of group index
for each frequency.
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V. Calculated linear transmission spectra of the metasurface with different structural
parameters
Using the commercial finite element method (FEM) solver of COMSOL Multiphysics, we
calculated the linear transmission spectra of the metasurface with different structure parameters.
The linear transmission spectra of the metasurface was defined as the quotient between the output
power flow of the metasurface with gold periodic nanostructures to that of the metasurface
without gold periodic nanostructures.
1) For different gold dimer periods
Figure S2 shows the calculated linear transmission spectra of the metasurface with different
gold dimer periods. With the increase of the period of the gold dimer, the transparency window
center of the metamaterial-induced transparency also has an obvious red-shift, and the left valley
(i.e. in the shorter wavelength) adjacent to the transparency peak becomes shallow. Because the
left valley is mainly contributed by the outer corners of the gold dimmer interaction (see Fig. 2c);
while the right valley is mainly caused by the inner corners of the gold dimmers interaction (see
Fig. 2e).
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1.0
0.5
0.0
1.0
900 nm
0.5
Transmission
0.0
1.0
950 nm
0.5
0.0
1.0
1000 nm
0.5
0.0
1.0
1050 nm
0.5
0.0
1.0
1100 nm
0.5
0.0
1150 nm
1200
1400
Wavelength (nm)
1600
Figure S2. Calculated linear transmission spectra of the metasurface with different gold
dimer periods. The blue, red, green, purple and yellow lines correspond to the period of 900 nm,
950 nm, 1000 nm, 1050 nm, and 1100 nm for the unit cell, respectively.
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2) For different lateral lengths of gold nanoprisms
Figure S3 shows the calculated transmission spectra of the metasurface with different lateral
lengths of gold nanoprisms. With increase of the lateral length, the metamaterial-induced
transparency peak has a little red-shift.
1.0
0.5
350
0.0
1.0
Transmission
0.5
0.0
1.0
380
0.5
400
0.0
1.0
0.5
0.0
1.0
420
0.5
0.0
450
1200
1300
1400
Wavelength (nm)
1500
Figure S3. Calculated linear transmission spectra of the metasurface with different lateral
lengths of gold nanoprisms. The blue, red, green, purple, and yellow lines corresponds to lateral
lengths of gold nanoprisms of 350 nm, 380 nm, 400 nm, 420 nm, and 450 nm for the unit cell,
respectively.
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3) For different gold nanoprism thicknesses
Figure S4 shows the calculated transmission spectra of the metasurface with different gold
nanoprism thicknesses. When the gold nanoprism thickness is 10 nm, which is less than that of
the optical thick, no metamaterial-induced transparency has been obtained. When the gold
nanoprism thickness is more than 20 nm, the metamaterial-induced transparency is obtained.
With the increase of the gold nanoprism thickness from 20 nm to 100 nm, the metamaterialinduced transparency is insensitive to thickness changes, and it becomes a little narrower with the
increase of the thickness, which permits the fabrication process has larger error for the thickness.
1.0
0.5
0.0
1.0
10
Transmission
0.5
0.0
1.0
20
0.5
0.0
1.0
40
0.5
0.0
1.0
60
0.5
0.0
100
1100
1200
1300
1400
Wavelength (nm)
1500
Figure S4. Calculated linear transmission spectra of the metasurface with different gold
nanoprism thickness of 20 nm, 40 nm, 60 nm, 80 nm and 100 nm, respectively.
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4) For different incident polarizations
Figure S5 shows the calculated transmission spectra of the metasurface with different incident
polarizations. The angles are formed by the electric field of the incident light away from the X
axis. For example, the 00 case corresponds to the incident light only possessing Ex component,
while 900 case corresponds to the incident light only possessing Ey component. With the increase
of the incident light angle away from the X-axis, the transparency window width becomes small
and the left valley (adjacent to the transparency peak) becomes deep, while the transparency
window peak is invariant. When the polarization angle is 120, the valleys beside the transparency
window have near depth.
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1.0
0.5
0.0
1.0
0
0.5
Transmission
0.0
1.0
30
0.5
0.0
1.0
60
0.5
0.0
1.0
90
0.5
0.0
1.0
120
0.5
0.0
150
1100 1200 1300 1400 1500 1600
Wavelength (nm)
Figure S5. Calculated linear transmission spectrum of the metasurface with different
incident polarization cases. The angles are formed by the electric field of the incident light
away from the X axis. For example, the 00 case corresponds to the incident light only possessing
Ex component, while 900 case corresponds to the incident light only possessing Ey component.
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VI. Optical interference experiment setup and measurements
The basic thought for measurement of the time delay is the optical interference, as shown in
Figure S6. A beam (with pulse duration of 35 fs and a repetition rate of 1 kHz) from a
femtosecond optical parameter amplifier system (model Opera Solo, Coherent Company, USA)
was split into two beams with a ratio of 10:1. Both the probe and pump light were Y-polarized
waves. The intensity of the probe light was attenuated to be less than 10 W/cm 2, so that the
influence of the probe light on the refractive index change of metasurface can be neglected. The
weak beam, as the probe light, was split into two beams (B_pro1 and B_pro2), they propagate
two ITO glasses, and the optical pathways were tuned to be equal. sA delay line was used to
adjust the optical path of B_pro1 and B_pro2 till the interference fringes appeared on the CCD
screen. And then one ITO glass in beam B_pro2 was replaced by our sample, the CCD images
were recorded at different time by adjusting the delay line till the interference fringes appeared.
The strong beam, used as the pump light (B_pum), was also incident on this upper-surface plane
and focused with a spot size of about 100 μm. There was a angle of about 30°between the
beams B_pum and B_pro2.
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Figure S6. Slow light measurement experimental setup.
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VII. Femtosecond pump-probe experiment setup and measurement process
The femtosecond pump-probe experiment setup is shown in Fig. S7. A beam (with a pulse
duration of 35 fs and a repetition rate of 1 kHz) from a femtosecond optical parameter amplifier
system (model Opera Solo, Coherent Company, USA) was split into two beams with a ratio of
10:1. Both the probe and pump light were Y-polarized waves. The intensity of the probe light
was attenuated to be less than 10 W/cm2, so that the influence of the probe light on the refractive
index change of ZnO/graphene and polycrystalline ITO can be neglected. The weak beam, as the
probe light, was incident normal to the upper-surface plane of the metamaterial with a spot size of
about 100 μm. The strong beam, used as the pump light, was also incident on this upper-surface
plane and focused with a spot size of about 200 μm. There was a small angle of 150 between the
pump and probe light. The probe light was in the center of the pump light when propagating
through the metamaterial sample. The probe light propagating through the metamaterial was
detected using a fiber monochromator (Model NIR-512, Ocean Optics, USA) with a resolution of
0.74 nm, the output signal of which was collected and analyzed by a computer. A delay line was
used to adjust the timing between the pump and probe pulses. According to the third-order
nonlinear optical Kerr effect, the effective refractive index n of the ZnO-nanograins/graphene
micro-sheets can be obtained by the relation
n  n0  n2 I
(7)
where n0 and n2 are effective linear and nonlinear refractive indices of the ZnOnanograins/graphene micro-sheets. I is the pump intensity.
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Femtosecond laser system
Figure S7. Optical pump-probe experimental setup.
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VIII. Closed-aperture Z-scan measurements and discussion of nonlinearity
A 35 fs, 1550 nm laser beam from a femtosecond optical parameter amplifier system (model
Opera Solo, Coherent Company, USA) with a repetition rate of 1 kHz was used as the light
source. The experimental measurement setup was as detailed in Ref. S5. The remarkable peak–
valley profile of the curve implies the negative value of the effective nonlinear refractive index n2
of the 180-nm-thick polycrystalline ITO film covered with multilayer-graphene micro-sheets.
The normalized transmission can be fitted toS5
T ( z)  1 
4x
( x  9)( x 2  1)
2
(8)
where T is the normal transmittance, x = z/z0 , z is the longitudinal distance from point, z0 is the
Rayleigh range of the laser beam, and ∆φ is the phase change. The effective nonlinear refractive
index n2 could be obtained from1
n2 

2I 0 (1  e L )
(9)
where λ is the laser wavelength in vacuum, α is the linear absorption index, I0 is the peak
intensity of the laser beam, and L is the sample thickness.
The measured results are shown in Figure S8. The nonlinear refractive index is -7.64×10-10
cm2/W for ITO glass with monolayer graphene on. When the ZnO nanoparticles were coated on
the monolayer graphene film, the nonlinear refractive index was increased to -1.07×10-9 cm2/W,
the nonlinear improvement of 1.4 times was mainly brought by the quantum confinement. In
addition, we also measured the nonlinear refractive index of the multilayer-graphene microsheets
on ITO glass using the same Z-scan method; it was -2.06×10-8 cm2/W, so the nonlinearity
improvement is obvious (about 27 times compared with that of the monolayer graphene) for the
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reinforced interaction provided by the multiayer-graphene microsheets. As we know, the final
nonlinear refractive index was -8.03×10-7 cm2/W for the complex films in our sample, the 39
times improvement of nonlinearity compared with that of the multilayer-graphene microsheets
were mainly contributed from the hot electron injection and surface plasmon polariton resonances.
Figure S8. Measured closed-aperture Z-scan curves. (a) SEM image of the ITO film covered
with monolayer graphene. (b) Corresponding measured closed-aperture Z-scan curve. (c) SEM
image of the ITO film covered with monolayer graphene and ZnO nanoparticles. (d)
Corresponding measured closed-aperture Z-scan curve for the film. The red solid curve is the
theoretical fit to the data.
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VIIII. AFM images for ZnO nanoparticles on ITO nanograin film and gold film
Both of ZnO and ITO appear nanograin shapes, so can provide strong quantum-size
confinement effects, which largely improves the nonlinear refractive index.
a
b
Figure S9. AFM images for ZnO nanoparticles on ITO nanograin film (a) and gold film (b).
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